Fix 3d plots in examples

[linpy.git] / linpy / polyhedra.py

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index bfc7efe..9e740a4 100644 (file)
--- a/linpy/polyhedra.py
+++ b/linpy/polyhedra.py
@@ -16,29 +16,35 @@
 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
 
 import functools
 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
 
 import functools

-import math

 import numbers
 
 from . import islhelper
 
 import numbers
 
 from . import islhelper
 

-from .islhelper import mainctx, libisl
+from .domains import Domain

 from .geometry import GeometricObject, Point
 from .geometry import GeometricObject, Point

+from .islhelper import libisl, mainctx

 from .linexprs import LinExpr, Rational
 from .linexprs import LinExpr, Rational

-from .domains import Domain

 
 
 __all__ = [
 
 
 __all__ = [

+    'Empty',
+    'Eq',
+    'Ge',
+    'Gt',
+    'Le',
+    'Lt',
+    'Ne',

     'Polyhedron',
     'Polyhedron',

-    'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
-    'Empty', 'Universe',
+    'Universe',

 ]
 
 
 class Polyhedron(Domain):
     """
     A convex polyhedron (or simply "polyhedron") is the space defined by a
 ]
 
 
 class Polyhedron(Domain):
     """
     A convex polyhedron (or simply "polyhedron") is the space defined by a

-    system of linear equalities and inequalities. This space can be
-    unbounded.
+    system of linear equalities and inequalities. This space can be unbounded.
+    A Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
+    points in a convex polyhedron.

     """
 
     __slots__ = (
     """
 
     __slots__ = (


@@ -50,34 +56,38 @@ class Polyhedron(Domain):
 
     def __new__(cls, equalities=None, inequalities=None):
         """
 
     def __new__(cls, equalities=None, inequalities=None):
         """

-        Return a polyhedron from two sequences of linear expressions: equalities
-        is a list of expressions equal to 0, and inequalities is a list of
-        expressions greater or equal to 0. For example, the polyhedron
+        Return a polyhedron from two sequences of linear expressions:
+        equalities is a list of expressions equal to 0, and inequalities is a
+        list of expressions greater or equal to 0. For example, the polyhedron

         0 <= x <= 2, 0 <= y <= 2 can be constructed with:
 
         >>> x, y = symbols('x y')
         0 <= x <= 2, 0 <= y <= 2 can be constructed with:
 
         >>> x, y = symbols('x y')

-        >>> square = Polyhedron([], [x, 2 - x, y, 2 - y])
+        >>> square1 = Polyhedron([], [x, 2 - x, y, 2 - y])
+        >>> square1
+        And(0 <= x, x <= 2, 0 <= y, y <= 2)

 
         It may be easier to use comparison operators LinExpr.__lt__(),
 
         It may be easier to use comparison operators LinExpr.__lt__(),

-        LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(),
-        Le(), Eq(), Ge() and Gt(), using one of the following instructions:
+        LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or
+        functions Lt(), Le(), Eq(), Ge() and Gt(), using one of the following
+        instructions:

 
         >>> x, y = symbols('x y')
 
         >>> x, y = symbols('x y')

-        >>> square = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
-        >>> square = Le(0, x, 2) & Le(0, y, 2)
+        >>> square1 = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
+        >>> square1 = Le(0, x, 2) & Le(0, y, 2)

 
         It is also possible to build a polyhedron from a string.
 
 
         It is also possible to build a polyhedron from a string.
 

-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')

 
         Finally, a polyhedron can be constructed from a GeometricObject
 
         Finally, a polyhedron can be constructed from a GeometricObject

-        instance, calling the GeometricObject.aspolyedron() method. This way, it
-        is possible to compute the polyhedral hull of a Domain instance, i.e.,
-        the convex hull of two polyhedra:
-
-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
-        >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
-        >>> Polyhedron(square | square2)
+        instance, calling the GeometricObject.aspolyedron() method. This way,
+        it is possible to compute the polyhedral hull of a Domain instance,
+        i.e., the convex hull of two polyhedra:
+
+        >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+        >>> Polyhedron(square1 | square2)
+        And(0 <= x, 0 <= y, x <= y + 2, y <= x + 2, x <= 3, y <= 3)

         """
         if isinstance(equalities, str):
             if inequalities is not None:
         """
         if isinstance(equalities, str):
             if inequalities is not None:


@@ -90,15 +100,23 @@ class Polyhedron(Domain):
         sc_equalities = []
         if equalities is not None:
             for equality in equalities:
         sc_equalities = []
         if equalities is not None:
             for equality in equalities:

-                if not isinstance(equality, LinExpr):
-                    raise TypeError('equalities must be linear expressions')
-                sc_equalities.append(equality.scaleint())
+                if isinstance(equality, LinExpr):
+                    sc_equalities.append(equality.scaleint())
+                elif isinstance(equality, numbers.Rational):
+                    sc_equalities.append(Rational(equality).scaleint())
+                else:
+                    raise TypeError('equalities must be linear expressions '
+                                    'or rational numbers')

         sc_inequalities = []
         if inequalities is not None:
             for inequality in inequalities:
         sc_inequalities = []
         if inequalities is not None:
             for inequality in inequalities:

-                if not isinstance(inequality, LinExpr):
-                    raise TypeError('inequalities must be linear expressions')
-                sc_inequalities.append(inequality.scaleint())
+                if isinstance(inequality, LinExpr):
+                    sc_inequalities.append(inequality.scaleint())
+                elif isinstance(inequality, numbers.Rational):
+                    sc_inequalities.append(Rational(inequality).scaleint())
+                else:
+                    raise TypeError('inequalities must be linear expressions '
+                                    'or rational numbers')

         symbols = cls._xsymbols(sc_equalities + sc_inequalities)
         islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
         symbols = cls._xsymbols(sc_equalities + sc_inequalities)
         islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)


@@ -136,7 +154,7 @@ class Polyhedron(Domain):
 
     def isuniverse(self):
         islbset = self._toislbasicset(self.equalities, self.inequalities,
 
     def isuniverse(self):
         islbset = self._toislbasicset(self.equalities, self.inequalities,

-            self.symbols)
+                                      self.symbols)

         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         libisl.isl_basic_set_free(islbset)
         return universe
         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         libisl.isl_basic_set_free(islbset)
         return universe


@@ -168,9 +186,9 @@ class Polyhedron(Domain):
 
     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
 
     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)

-            for equality in self.equalities]
+                      for equality in self.equalities]

         inequalities = [inequality.subs(symbol, expression)
         inequalities = [inequality.subs(symbol, expression)

-            for inequality in self.inequalities]
+                        for inequality in self.inequalities]

         return Polyhedron(equalities, inequalities)
 
     def asinequalities(self):
         return Polyhedron(equalities, inequalities)
 
     def asinequalities(self):


@@ -210,6 +228,10 @@ class Polyhedron(Domain):
 
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
 
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):

+        if bool(libisl.isl_basic_set_is_empty(islbset)):
+            return Empty
+        if bool(libisl.isl_basic_set_is_universe(islbset)):
+            return Universe

         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []


@@ -218,8 +240,8 @@ class Polyhedron(Domain):
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):

-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
-                    libisl.isl_dim_set, index)
+                coefficient = libisl.isl_constraint_get_coefficient_val(
+                    islconstraint, libisl.isl_dim_set, index)

                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient
                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient


@@ -244,26 +266,28 @@ class Polyhedron(Domain):
         islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
         islls = libisl.isl_local_space_from_space(islsp)
         for equality in equalities:
         islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
         islls = libisl.isl_local_space_from_space(islsp)
         for equality in equalities:

-            isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
+            isleq = libisl.isl_equality_alloc(
+                libisl.isl_local_space_copy(islls))

             for symbol, coefficient in equality.coefficients():
                 islval = str(coefficient).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 index = indices[symbol]
             for symbol, coefficient in equality.coefficients():
                 islval = str(coefficient).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 index = indices[symbol]

-                isleq = libisl.isl_constraint_set_coefficient_val(isleq,
-                    libisl.isl_dim_set, index, islval)
+                isleq = libisl.isl_constraint_set_coefficient_val(
+                    isleq, libisl.isl_dim_set, index, islval)

             if equality.constant != 0:
                 islval = str(equality.constant).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
             islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
         for inequality in inequalities:
             if equality.constant != 0:
                 islval = str(equality.constant).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
             islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
         for inequality in inequalities:

-            islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
+            islin = libisl.isl_inequality_alloc(
+                libisl.isl_local_space_copy(islls))

             for symbol, coefficient in inequality.coefficients():
                 islval = str(coefficient).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 index = indices[symbol]
             for symbol, coefficient in inequality.coefficients():
                 islval = str(coefficient).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
                 index = indices[symbol]

-                islin = libisl.isl_constraint_set_coefficient_val(islin,
-                    libisl.isl_dim_set, index, islval)
+                islin = libisl.isl_constraint_set_coefficient_val(
+                    islin, libisl.isl_dim_set, index, islval)

             if inequality.constant != 0:
                 islval = str(inequality.constant).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)
             if inequality.constant != 0:
                 islval = str(inequality.constant).encode()
                 islval = libisl.isl_val_read_from_str(mainctx, islval)


@@ -313,19 +337,12 @@ class Polyhedron(Domain):
         else:
             return 'And({})'.format(', '.join(strings))
 
         else:
             return 'And({})'.format(', '.join(strings))
 

-    def _repr_latex_(self):
-        strings = []
-        for equality in self.equalities:
-            strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
-        for inequality in self.inequalities:
-            strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
-        return '$${}$$'.format(' \\wedge '.join(strings))
-

     @classmethod
     @classmethod

-    def fromsympy(cls, expr):
-        domain = Domain.fromsympy(expr)
+    def fromsympy(cls, expression):
+        domain = Domain.fromsympy(expression)

         if not isinstance(domain, Polyhedron):
         if not isinstance(domain, Polyhedron):

-            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+            raise ValueError('non-polyhedral expression: {!r}'.format(
+                expression))

         return domain
 
     def tosympy(self):
         return domain
 
     def tosympy(self):


@@ -359,9 +376,6 @@ class EmptyType(Polyhedron):
     def __repr__(self):
         return 'Empty'
 
     def __repr__(self):
         return 'Empty'
 

-    def _repr_latex_(self):
-        return '$$\\emptyset$$'
-

 Empty = EmptyType()
 
 
 Empty = EmptyType()
 
 


@@ -382,83 +396,86 @@ class UniverseType(Polyhedron):
     def __repr__(self):
         return 'Universe'
 
     def __repr__(self):
         return 'Universe'
 

-    def _repr_latex_(self):
-        return '$$\\Omega$$'
-

 Universe = UniverseType()
 
 
 def _pseudoconstructor(func):
     @functools.wraps(func)
 Universe = UniverseType()
 
 
 def _pseudoconstructor(func):
     @functools.wraps(func)

-    def wrapper(expr1, expr2, *exprs):
-        exprs = (expr1, expr2) + exprs
-        for expr in exprs:
-            if not isinstance(expr, LinExpr):
-                if isinstance(expr, numbers.Rational):
-                    expr = Rational(expr)
+    def wrapper(expression1, expression2, *expressions):
+        expressions = (expression1, expression2) + expressions
+        for expression in expressions:
+            if not isinstance(expression, LinExpr):
+                if isinstance(expression, numbers.Rational):
+                    expression = Rational(expression)

                 else:
                     raise TypeError('arguments must be rational numbers '
                 else:
                     raise TypeError('arguments must be rational numbers '

-                        'or linear expressions')
-        return func(*exprs)
+                                    'or linear expressions')
+        return func(*expressions)

     return wrapper
 
     return wrapper
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Lt(*exprs):
+def Lt(*expressions):

     """
     Create the polyhedron with constraints expr1 < expr2 < expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 < expr2 < expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(right - left - 1)
     return Polyhedron([], inequalities)
 
         inequalities.append(right - left - 1)
     return Polyhedron([], inequalities)
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Le(*exprs):
+def Le(*expressions):

     """
     Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(right - left)
     return Polyhedron([], inequalities)
 
         inequalities.append(right - left)
     return Polyhedron([], inequalities)
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Eq(*exprs):
+def Eq(*expressions):

     """
     Create the polyhedron with constraints expr1 == expr2 == expr3 ...
     """
     equalities = []
     """
     Create the polyhedron with constraints expr1 == expr2 == expr3 ...
     """
     equalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         equalities.append(left - right)
     return Polyhedron(equalities, [])
 
         equalities.append(left - right)
     return Polyhedron(equalities, [])
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Ne(*exprs):
+def Ne(*expressions):

     """
     Create the domain such that expr1 != expr2 != expr3 ... The result is a
     Domain object, not a Polyhedron.
     """
     domain = Universe
     """
     Create the domain such that expr1 != expr2 != expr3 ... The result is a
     Domain object, not a Polyhedron.
     """
     domain = Universe

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         domain &= ~Eq(left, right)
     return domain
 
         domain &= ~Eq(left, right)
     return domain
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Ge(*exprs):
+def Ge(*expressions):

     """
     Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(left - right)
     return Polyhedron([], inequalities)
 
         inequalities.append(left - right)
     return Polyhedron([], inequalities)
 

+

 @_pseudoconstructor
 @_pseudoconstructor

-def Gt(*exprs):
+def Gt(*expressions):

     """
     Create the polyhedron with constraints expr1 > expr2 > expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 > expr2 > expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(left - right - 1)
     return Polyhedron([], inequalities)
         inequalities.append(left - right - 1)
     return Polyhedron([], inequalities)